A monopoly faces two groups of consumers. Group one'sdemand curve is 1=160.51,Group two'sdemand curve 2=140.52. The monopoly's total cost function is given by ()=6.

(1) If the monopolist can engage in third-degree price discriminationby charging different prices to the two groups, what should be the price and quantity in each market?

(2) If the monopolisthas to charge the sameprice to all consumers, what is the optimal price?